Answer :
To factor the expression [tex]\(8x^9 + 4x^6 + 28\)[/tex] completely by pulling out the Greatest Common Factor (GCF), we follow these steps:
1. Identify the GCF:
Look at each term in the expression: [tex]\(8x^9\)[/tex], [tex]\(4x^6\)[/tex], and [tex]\(28\)[/tex]. We notice that the coefficients are 8, 4, and 28.
2. Determine the GCF of the coefficients:
The numbers 8, 4, and 28 have a common factor of 4. This is the greatest number that divides each coefficient.
3. Factor out the GCF:
Now, rewrite the entire expression by factoring out the GCF (4) from each term:
[tex]\[
8x^9 + 4x^6 + 28 = 4(2x^9) + 4(x^6) + 4(7)
\][/tex]
[tex]\[
= 4(2x^9 + x^6 + 7)
\][/tex]
4. Recheck each factor:
Make sure each term inside the parentheses does not have any further common factors. In this case, [tex]\(2x^9 + x^6 + 7\)[/tex] doesn't have any common factors other than 1.
So, the completely factored form of the expression [tex]\(8x^9 + 4x^6 + 28\)[/tex] by pulling out the GCF is:
[tex]\[
4(2x^9 + x^6 + 7)
\][/tex]
1. Identify the GCF:
Look at each term in the expression: [tex]\(8x^9\)[/tex], [tex]\(4x^6\)[/tex], and [tex]\(28\)[/tex]. We notice that the coefficients are 8, 4, and 28.
2. Determine the GCF of the coefficients:
The numbers 8, 4, and 28 have a common factor of 4. This is the greatest number that divides each coefficient.
3. Factor out the GCF:
Now, rewrite the entire expression by factoring out the GCF (4) from each term:
[tex]\[
8x^9 + 4x^6 + 28 = 4(2x^9) + 4(x^6) + 4(7)
\][/tex]
[tex]\[
= 4(2x^9 + x^6 + 7)
\][/tex]
4. Recheck each factor:
Make sure each term inside the parentheses does not have any further common factors. In this case, [tex]\(2x^9 + x^6 + 7\)[/tex] doesn't have any common factors other than 1.
So, the completely factored form of the expression [tex]\(8x^9 + 4x^6 + 28\)[/tex] by pulling out the GCF is:
[tex]\[
4(2x^9 + x^6 + 7)
\][/tex]
